answer the following question in details.

Use a general reasoning argument to construct Thiele's differential equation for a regular premium n -year term assurance for a life aged x by considering the change in reserves over a short time period. Assume that: interest is earned continuously at force of interest 8; premiums are payable continuously at rate P on pa; and the sum assured of 1 is payable immediately on death. [5]Suppose a firm in monopolistic competition is in long-run equilibrium. What is the effect on the firm's output, price and profit in the short run and in the long run of: (i) a rise in the firm's fixed costs of production, eg an increase in rent [5] (ii) a decrease in the firm's variable costs of production, eg a reduction in wages. [5] [Total 101